muranks {crank}

Complete a matrix of rankings

Description

Fills an incomplete matrix of rankings with means of unallocated ranks

Usage

 muranks(x,allranks=NULL,rankx=FALSE)

Arguments

x

A vector or matrix of rankings that may contain ties and NAs. Objects ranked are assumed to be columns and ranking methods rows.

allranks

An optional list of all ranks that might have been allocated. Defaults to the unique values in ‘⁠x⁠’.

rankx

Whether to apply the ‘⁠rank⁠’ function (see Details).

Details

‘⁠muranks⁠’ assumes that the values in ‘⁠x⁠’ are rankings with values in the set ‘⁠allranks⁠’ or if that is NULL, between 1 and the number of columns or values in ‘⁠x⁠’. If any values in ‘⁠x⁠’ are outside this range, or if the missing ranks are not sequential, the function will drop that row with a warning.

For each row, the function finds the mean of those ranks in ‘⁠allranks⁠’ that were not allocated and substitutes that value for any missing values in the row.

If ‘⁠rankx⁠’ is TRUE, each row is passed to ‘⁠rank⁠’. This will convert competition ranks or any set of numbers to the usual mean rankings. This will also override the rejection of rows in which the missing ranks are not sequential, and may produce counterintuitive imputed ranks.

Value

A matrix similar to ‘⁠x⁠’ in which any NAs are replaced by the mean of unallocated ranks for each row.

Note

‘⁠muranks⁠’ will impute ranks for "best/worst" ranking, where the method (rater) allocates the highest ranks to the most preferred data objects and the lowest ranks to the least preferred. The mean of all unallocated ranks is imputed for unranked data objects. It is assumed that unranked data objects are considered less preferred than those allocated high ranks, more preferred than those allocated low ranks, and not differentiated from each other. If this assumption is not satisfied, ‘⁠muranks⁠’ will warn the operator that one or more rows have been dropped. To explain this behavior, consider the case in which a method allocates the ranks 1,2,3,5,7,8 to eight data objects. Two ranks have not been allocated, 4 and 6. It would be possible to impute the mean, 5, to both, but this ignores the implicit information that the two data objects were differentiated by the rank 5, which is "between" them. Only in the unlikely case that both were considered equivalent to the object ranked 5 would this be correct, as there is no way to establish which was more or less preferred. The operator should be aware that if ‘⁠rankx⁠’ is TRUE, the unranked objects will be allocated the lowest ranks, which is unlikely to be correct.

Author(s)

Jim Lemon

See Also

meanranks,rank

Examples

 # simulate ranking from the top with variable completion
 x<-matrix(NA,nrow=10,ncol=10)
 for(i in 1:10) {
  nx<-sample(2:10,1)
  xx<-sample(1:10,nx)
  x[i,xx]<-1:nx
 }
 x
 muranks(x)